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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Resultantal varieties related to zeroes of L-functions of Carlitz modules

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Grishkov, A. [1] ; Logachev, D. [2]
Total Authors: 2
[1] Univ Sao Paulo, Dept Matemat & Estat, BR-05508 Sao Paulo - Brazil
[2] Univ Fed Amazonas, ICE, DM, Manaus, Amazonas - Brazil
Total Affiliations: 2
Document type: Journal article
Source: FINITE FIELDS AND THEIR APPLICATIONS; v. 38, p. 116-176, MAR 2016.
Web of Science Citations: 1

We show that there exists a connection between two types of objects: some kind of resultantal varieties over C, from one side, and varieties of twists of the tensor powers of the Carlitz module such that the order of 0 of its L-functions at infinity is a constant, from another side. Obtained results are only a starting point of a general theory. We can expect that it will be possible to prove that the order of 0 of these L-functions at 1 (i.e. the analytic rank of a twist) is not bounded - this is the function field case analog of the famous conjecture on non-boundedness of rank of twists of an elliptic curve over Q. The paper contains a calculation of a relevant polynomial determinant. (C) 2015 Published by Elsevier Inc. (AU)

FAPESP's process: 13/10596-8 - Algebraic loops and Drinfeld modules
Grantee:Alexandre Grichkov
Support Opportunities: Research Grants - Visiting Researcher Grant - International